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    Square Lattice

    Image

    Image

    Common name

    2-dimensional cubic lattice

    Description of lattice

    basis | (1 | 0) | (0 | 1) Gram matrix | (1 | 0 0 | 1)

    Lattice invariants

    dimension | 2 determinant | 1 minimal squared norm | 1 smallest vectors | (1 | 0) | (0 | 1) | (-1 | 0) | (0 | -1) kissing number | 4

    Lattice-packing invariants

    packing radius | 1/2 = 0.5 covering radius | 1/sqrt(2)≈0.707107 density | π/4≈0.785398 center density | 1/4 = 0.25 Hermite invariant | 1 thickness | π/2≈1.5708 volume | 1

    Quadratic form and theta series

    quadratic form | x^2 + y^2 theta series (closed series) | ϑ_3(0, e^(i π x))^2

    More properties

    dual | integer lattice | 2 modular number | 1 number of symmetries | 8

    Common properties

    integral | odd | unimodular

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